Can I say "Termination approved" or "Termination signed" on the letter?

You can, but choose wording that accurately reflects what actually happened and that is appropriate for the recipient and legal context. Short guidance:

• If someone formally approved the termination (but did not sign the letter): write "Termination approved" or "Termination approved by [name/position]" (include date if helpful).
• If someone physically or electronically signed the letter: write "Termination signed" or "Signed on [date] by [name/position]".
• If both occurred and you want to show both actions: "Termination approved and signed by [name/position] on [date]."
• If you must be precise for legal/employment reasons, prefer full phrasing: "This termination was approved by [name/position] on [date] and the termination letter was signed by [name/position] on [date]."

Avoid ambiguous single-word notes on formal records. If in doubt about legal implications, consult HR or legal counsel before finalizing wording.